Lloyd's insurer Chaucer called for a truce with its Names after increasing its offer for unaligned 2004 capacity on Syndicate 1084 after its proposed merger.
It raised the price it is prepared to pay to 11p a pound from 7.5p.
Chaucer's offer was conditional on it receiving acceptances from Names holding more than 50% of the non-aligned capacity. Otherwise the price would revert to 7.5p per pound.
The offer arose following Chaucer's plans to merge Syndicates 587 and 1096 into Syndicate 1084 for the 2004 year of account.
Some Names had argued the proposed merger lowered the value of their capacity rights by denying them the chance to place their investment on a focused syndicate.
They said Chaucer's price compared poorly to offers made last year by Amlin, at 20p, and Catlin, at 43p.
Chaucer is one of a dwindling number of insurers accepting investment from Names.
Chaucer Holdings' managing director Ewen Gilmour denied the merger was a move against Names. It was needed to enable the free movement of capital and to gain the scale needed to appeal to US investors.
"We aren't remotely anti-Names," he said.